matlab代码实现动态贝叶斯网络

动态贝叶斯网络（Dynamic Bayesian Network，DBN）是贝叶斯网络的一种扩展，用于建模具有时间依赖性的动态系统。在DBN中，节点的状态不仅依赖于其父节点的状态，还依赖于前一个时间步的节点状态。

下面是一个用Matlab实现动态贝叶斯网络的简单示例代码：

classdef DBN
    properties
        numNodes   % 节点数量
        numStates  % 每个节点的状态数量
        prior      % 初始状态概率 P(X_1)
        transition % 状态转移概率 P(X_t | X_t-1)
        emission   % 观测概率 P(E_t | X_t)
    end
    
    methods
        function obj = DBN(numNodes, numStates)
            obj.numNodes = numNodes;
            obj.numStates = numStates;
            obj.prior = zeros(1, numStates);
            obj.transition = zeros(numStates, numStates);
            obj.emission = zeros(numStates, numNodes);
        end
        
        function obj = setPrior(obj, prior)
            obj.prior = prior;
        end
        
        function obj = setTransition(obj, transition)
            obj.transition = transition;
        end
        
        function obj = setEmission(obj, emission)
            obj.emission = emission;
        end
        
        function likelihood = forward(obj, evidence)
            T = size(evidence, 2);
            likelihood = zeros(obj.numStates, T);
            
            % 初始化t=1的前向概率
            likelihood(:, 1) = obj.prior' .* obj.emission(:, evidence(1));
            
            % 递推计算t=2:T的前向概率
            for t = 2:T
                likelihood(:, t) = (obj.transition' * likelihood(:, t-1)) .* obj.emission(:, evidence(t));
            end
        end
        
        function posterior = backward(obj, evidence)
            T = size(evidence, 2);
            posterior = zeros(obj.numStates, T);
            
            % 初始化t=T的后向概率
            posterior(:, T) = ones(obj.numStates, 1);
            
            % 递推计算t=T-1:-1:1的后向概率
            for t = T-1:-1:1
                posterior(:, t) = obj.transition * (posterior(:, t+1) .* obj.emission(:, evidence(t+1)));
            end
        end
        
        function [prior, transition, emission] = learnParameters(obj, evidence)
            T = size(evidence, 2);
            
            % 初始化参数
            prior = zeros(1, obj.numStates);
            transition = zeros(obj.numStates, obj.numStates);
            emission = zeros(obj.numStates, obj.numNodes);
            
            % 估计初始状态概率
            prior = obj.forward(evidence(:, 1));
            
            % 估计状态转移概率
            for t = 2:T
                transition = transition + obj.forward(evidence(:, t)) * obj.backward(evidence(:, t-1))';
            end
            transition = bsxfun(@rdivide, transition, sum(transition, 1));
            
            % 估计观测概率
            for t = 1:T
                emission(:, evidence(t)) = emission(:, evidence(t)) + obj.forward(evidence(:, t)) .* obj.backward(evidence(:, t));
            end
            emission = bsxfun(@rdivide, emission, sum(emission, 1));
        end
    end
end

使用示例：

% 创建一个有3个节点、每个节点有2个状态的DBN
dbn = DBN(3, 2);

% 设置初始状态概率
prior = [0.6, 0.4];
dbn = dbn.setPrior(prior);

% 设置状态转移概率
transition = [0.7, 0.3; 0.4, 0.6];
dbn = dbn.setTransition(transition);

% 设置观测概率
emission = [0.3, 0.7; 0.8, 0.2];
dbn = dbn.setEmission(emission);

% 根据观测数据学习参数
evidence = [1, 2, 2, 1];
[prior_estimated, transition_estimated, emission_estimated] = dbn.learnParameters(evidence);

这个代码实现了一个简单的动态贝叶斯网络类，其中包含了设置参数、前向传播、后向传播和参数学习等方法。你可以根据需要对该类进行扩展，添加更多的功能和方法。